Class 6 Operations on whole Numbers Exercise 4.5-1

\begin{array}{l} \text {Q1. Without drawing a diagram, find } \\ (i) \quad 10^{\text {th }} \text { square number} \\ (ii) \quad 6^{\text {th }} \text { triangular number} \\ \\\text {Sol. } (i) \quad 10^{\text {th }} \text { square number} \\ \text {Nth square number } =n \times n \\ \therefore 10^{\text {th }} \text { square number } =10 \times 10=100 \\ \\(ii) \quad 6^{\text {th }} \text { triangular number} \\ \text {Nth triangular number }=n \times {\large \frac {(n+1)}{2} } \\ \therefore 6^{\text {th }} \text { triangular number} =6 \times {\large \frac {(6+1)}{2} } =21 \\ \\\text {Q2. (i) Can a rectangular number also be a square number?} \\ \\ \text {(ii) Can a triangular number also be a square number? } \\ \\\text {Sol. (i) Yes. A rectangular number can also be a square number.} \\ \text {For example, 16 is a rectangular number which can also be a square number.} \\ \\ \end{array}\begin{array}{cc} & \bigstar & \bigstar \\ & \bigstar & \bigstar \\ & \bigstar & \bigstar \\ & \bigstar & \bigstar \\ & \bigstar & \bigstar \\ & \bigstar & \bigstar \\ & \bigstar & \bigstar \\ & \bigstar & \bigstar \\ \end{array} \begin{array}{l} \text {And } \\ \end{array} \begin{array}{cccc} & \bigstar & \bigstar & \bigstar & \bigstar\\ & \bigstar & \bigstar & \bigstar & \bigstar\\ & \bigstar & \bigstar & \bigstar & \bigstar\\ & \bigstar & \bigstar & \bigstar & \bigstar\\\end{array}\begin{array}{l} \text {(ii) Yes. A triangular number can also be a square number. } \\ \text {For example, 1 is a triangular number which can also be a square number.} \\ \\\text {Q3. Write the first four products of two numbers with difference } \\ \text {4 starting from in the following order:} \\1,2,3,4,5,6, \ldots \ldots \ldots \\\text {Identify the pattern in the products and write the next three products.} \\ \\\text {Sol. } \\ 1 \times 5=5 (5-1=4) \\ 2 \times 6=12 [\text {Here } 6-2=4 ] \\ 3 \times 7=21 [\text {Here } 7-3=4 ] \\ 4 \times 8=32 [\text {Here } 8-4=4 ] \\ \\\text {Q4. Observe the pattern in the following and fill in the blanks:} \\ 9 \times 9+7=88 \\ 98 \times 9+6=888 \\ 987 \times 9+5=8888 \\ 9876 \times 9+4=\ldots \ldots \\ 98765 \times 9+3=\ldots \ldots \\ 987654 \times 9+2=\ldots \ldots \\ 9876543 \times 9+1=\ldots \ldots \\ \\\text {Sol. } \quad 9 \times 9+7=88 \\ 98 \times 9+6=888 \\ 987 \times 9+5=8888 \\ 9876 \times 9+4=88888 \\ 98765 \times 9+3=8888888 \\ 987654 \times 9+2=8888888 \\ 9876543 \times 9+1=88888888 \\ \end{array}